Question

Residential building codes typically require the use of 12 - gauge copper wire (diameter 0.205 cm) for wiring receptacles. Such circuits carry currents as large as 20.0 A. If a wire of smaller diameter (with a higher gauge number) carried that much current, the wire could rise to a high temperature and cause a fire. (a) Calculate the rate at which internal energy is produced in 1.00 m of 12 - gauge copper wire carrying 20.0 A. (b) Repeat the calculation for a 12 - gauge aluminum wire. (c) Explain whether a 12 - gauge aluminum wire would be as

Answer 1

Answer:

a. 2.92*10^{-12}J/s

b. 4.82*10^{-12}J/s

Explanation:

You can use the expression for the rate of energy produce per unit time

$E_i=\rho \frac{l}{S}I^2$

where

rho: resistivity

I: current

l: length

you can also use that

resistivity cooper=18.35*10^{-19}ohm*m

resistivity aluminum=30.31*10^{-19}ohm*m

(a) cooper

$E_c=(18.35*10^{-19}\Omega m)\frac{1.0m}{\pi (0.002m)^2}(20.0A)=2.92*10^{-12}\frac{J}{s}$

(b) aluminum

$E_c=(30.31*10^{-19}\Omega m)\frac{1.0m}{\pi (0.002m)^2}(20.0A)=4.82*10^{-12}\frac{J}{s}$

(c) Aluminum produced more energy due to that its density and its resistivity are greater than for cooper

hope this helps!!